(d), (e) Calculations of the 18 σ-transition frequencies in the presence of a 69 μ T bias field, including the influence of Clebsch-Gordan coefficients. Here Fourier-limited transition linewidths of 10 Hz are used. The relative transition amplitudes for the different sublevels are strongly influenced by the Clebsch-Gordan coefficients. The peaks are labeled by the ground-state sublevel of the transition. (b), (c) Data are shown in gray and fits are shown as solid lines. (c) Observation of the 18 σ transitions when the probe laser polarization is orthogonal to that of the lattice ( θ = π / 2) when a field of 69 μ T is used. (b) Observation of the S 1 0 − P 3 0 π transitions when θ = 0 in the presence of a 58 μ T magnetic field. The hyperfine interaction state mixing modifies the P 3 0 g factor, making the magnitude about 60% larger than that of S 1 0. The large nuclear spin ( I = 9 / 2 for Sr 87) results in 28 total transitions, and the labels π, σ +, and σ − represent transitions where m F changes by 0, + 1, and − 1, respectively. The probe laser propagates colinearly with the lattice beam and the linear probe polarization can be rotated relative to the quantization ( x) axis by an angle θ. The lattice laser propagates along the z axis and is linearly polarized along the x axis, parallel to the bias magnetic field such that φ ≈ π / 2. (a) Typical experimental field orientation for lattice spectroscopy. (e) Detection of the logic ion’s internal state via the electron-shelving technique (). (d) Resolved-sideband pulse on the red sideband of the logic ion, mapping the first excited motional state amplitude to the electronically excited state of the logic ion. (c) Resolved-sideband pulse on the blue sideband of the clock ion to the auxiliary state, mapping the ground-state amplitude onto the first excited motional state. (b) After clock interrogation, the spectroscopy ion is in an equal superposition of the two clock states. (a) Initially, both ions are prepared in the electronic and motional ground states. In addition, two vibrational levels ( | 0 ⟩ n, | 1 ⟩ n) of a common motional mode of the ions in the trap are shown. Shown are the clock ground ( S 1 0) and excited ( P 3 0) clock states and an auxiliary metastable state ( P 3 1) together with the logic ion (qubit states | ↓ ⟩ L, | ↑ ⟩ L). Measurement of the frequency of a poorly known optical frequency source (e.g., previously measured at the resolution of a wave meter) can be determined by measuring the heterodyne beat between the frequency source and the frequency comb. Thus, by stabilizing f CEO and f rep to a well-known frequency reference, each comb mode frequency is well known. In this interferometer, one comb mode ν n is frequency doubled and heterodyne beat with the comb mode at twice the frequency ν 2 n. f CEO is given by the frequency of one mode of the comb (e.g., ν n) modulo f rep, and can be measured and stabilized with a f − 2 f interferometer. The relative carrier-envelope phase in the time domain is related to the offset frequency f CEO in the frequency domain. Each tooth in the comb, a particular single-frequency mode, is separated from its neighbor by f rep. (b) By Fourier transformation to the frequency domain, the corresponding frequency comb spectrum is revealed. Another important degree of freedom is the phase difference between the envelope maximum and the underlying electric field oscillating at the carrier optical frequency. By simply rotating the microscope turret, the user can switch between optical and AFM modes quickly and accurately, maintaining the look and feel of optical microscopy in the AFM mode.(a) In the time domain, the laser output generates femtosecond pulse-width envelopes separated in time by 1 / f rep. bright-field, dark-field, polarization, fluorescence, etc.), the user can further determine the point-of-interest for the AFM measurement. Using additional illumination and detection techniques (e.g. Through the simultaneous sample and AFM-cantilever view, the measurement position can be easily identified and adjusted. The optical mode combined with an advanced video camera system allows high-resolution sample survey and quick selection of the area-of-interest. topography etc.) are displayed as an image.
The sample is scanned under the tip using a piezo-driven scanning-stage and the results (e.g.
The WITec Atomic Force Microscope integrated into a research-grade optical microscope provides superior optical access, exact cantilever alignment and high-resolution sample survey.
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